A square sheet of side ‘a’ is lying parallel to XY plane at z = a. The electric field in the region is $\vec{E} = {cz}^{2} \hat{k}$ . The electric flux through the sheet is

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$\frac{1}{3} a^{3} c$

$\frac{1}{3} a^{4} c$

$a^{4} c$

answer is A.

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Detailed Solution

Area vector for this square sheet, $\vec{A} = (a^{2}) k$
Electric field at square sheet at $(z = a), \vec{E} = c (a)^{2} k$
Electric flux through the sheet $ϕ = \vec{E} \cdot \vec{A} = (a^{2} k) \cdot ({ca}^{2} k) = {ca}^{4} (k \cdot k) = {ca}^{4}$

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